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(C) The equation of the radical axis of two circles $S_1 = 0$ and $S_2 = 0$ is given by $S_1 - S_2 = 0$.First,rewrite the equations in the form $x^2 +

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$7x - 8y - 14 = 0$

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(C) The equation of the radical axis of two circles $S_1 = 0$ and $S_2 = 0$ is given by $S_1 - S_2 = 0$.First,rewrite the equations in the form $x^2 + y^2 + 2gx + 2fy + c = 0$ with coefficient $1$ for $x^2$ and $y^2$.For the first circle: $2x^2 + 2y^2 - 7x = 0 \Rightarrow x^2 + y^2 - 3.5x = 0$.For the second circle: $x^2 + y^2 - 4y - 7 = 0$.Subtracting the two equations: $(x^2 + y^2 - 3.5x) - (x^2 + y^2 - 4y - 7) = 0$.$-3.5x + 4y + 7 = 0$.Multiply by $-2$ to clear the decimal: $7x - 8y - 14 = 0$.

The equation of the radical axis of the circles $2x^2 + 2y^2 - 7x = 0$ and $x^2 + y^2 - 4y - 7 = 0$ is

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